The laws, languages (except for Basque), many monuments, religion and trade of the Iberian Peninsula.
Explanation:
Romans reached the Iberian Peninsula in 218 BCE taking some Mediterranean coastal cities and gradually took over the entire Peninsula. Roman rule lasted until the 5th when Barbarians (mostly Germanic tribes) invaded Hispania.
Because Roman rule was so lasting it left a strong legacy through a process called Romanization. First it affected the upper classes but ended up spreading Roman culture to the myriad of peninsular tribes. Thus, Law is based on the Roman legal tradition; all Iberian languages (except Basque) descend from Latin; many Roman monuments and cities can be still found in both Portugal and Spain; Greek-Roman religion blended with the local religion, the growth and later prevalence of Christianism throughout Empire ensured the adoption of the Christian faith by the Hispano-Roman people; trade was also improved, with the usage of coins which were unknown or very scarce in the Celtic parts of the Peninsula (western half) when the Romans first arrived.